## a^2n +b^2n=c^2n

For students of class 11-12 (age 16+)
Rafe
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Joined: Wed Oct 24, 2012 11:25 am

### a^2n +b^2n=c^2n

Prove that if \$a^{2n}+b^{2n}=c^{2n}\$ where \$a,b,c\$ are positive,then \$a^n+b^n>c^n\$.Can you do it by geometry?
Last edited by *Mahi* on Tue Nov 06, 2012 10:34 pm, edited 2 times in total.
Reason: LaTeXed, use capital and small letters properly.

Phlembac Adib Hasan
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### Re: a^2n +b^2n=c^2n

Rafe wrote:PROVE THAT IF \$a^{2n}+b^{2n}=c^{2n}\$ WHERE \$a,b,c\$ ARE POSITIVE,THEN \$a^n+b^n>c^n\$. CAN YOU DO IT BY GEOMETRY
Use \$L^AT_EX\$ please, it makes our work a lot easier.
Let \$a^n=x,b^n=y,c^n=z\$. So the equation implies \$x^2+y^2=z^2\$
So from Pythagoras's theorem, it is possible to construct a right angled triangle with side lengths \$x,y,z\$ when \$z\$ is the hypotenuse. Now from triangle inequality, it easily follows \$x+y>z\$.
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